Many new IoT applications have emerged with the fast evolution of 5G and the Internet of Things (IoT). These applications place higher demands on network energy consumption and processing capabilities. Mobile edge computing (MEC) significantly enhances execution efficiency, while energy harvesting (EH) modules further augment the operational features of IoT devices. However, existing studies mainly concentrate on energy consumption and latency problems, often neglecting issues about user mobility and potential privacy leakage within the MEC environment. Therefore, optimizing computation offloading and resource allocation for MEC-enabled IoT networks is essential. This work proposes an innovative architecture with EH for collaborative computing between multiple mobile devices (MDs) and MEC servers. To tackle the problem, this work also proposes an advanced hybrid algorithm named Self-adaptive Bat Optimizer with Genetic operations and individual update of Grey wolf optimizer (SBG2). With SBG2, this work aims to minimize the energy consumption of MDs while providing user mobility and privacy protection. Simulation experiments show that SBG2 reduces energy consumption by 79.15%, 93.20%, and 89.58%, respectively, compared to the other three typical algorithms.